Hi Bruno,
> Again we are discussing the arithmetical realism (which I just assume).
A bold assumption, if I may say so.
> To be clear on that hypothesis, I do indeed find plausible that the
> number six is perfect, even in the case the "branes would not have
> collide, no big bang, no physical universe".
> Six is perfect just because its divisors are 1, 2, and 3; and that
> 1+2+3 = 6. Not because I know that. I blieve the contrary: it is the
> independent truth of "6 = sum of its proper divisors" than eventually
> I, and you, can learn it.
I understand your argumentation well, because maybe one or two years
ago I said nearly the same sentences to colleagues.
But my exploration into cognitive neuroscience has exposed to me
how mathematical thinking comes about, and that it is indeed not
separable from our human brains.
> If you want, numbers are what makes any counting possible.
Numbers are symbols we create in our minds to communicate with
fellow individuals about things of importance to us.
To paraphrase Descartes very liberally:
We group, therefore we can count.
Our act of arbitrary grouping (made a bit less arbitrary by
evolution, which makes us group things which are good to
our survival, like gazelles and spears or berries) let's us
count and communicate the number.
For the universe "one apple" may not exist, because in effect
there are only quarks interacting. And at this level indeterminacy
strikes mercilessly, making it all but meaningless to count quarks.
Also, concepts like infinity are most definitely not universal
concepts "out there", but products of our mind.
> It is not because some country put salt on pancakes that pancakes do
> not exist there. Roman where writing 8 -3 for us 8 - 2. It is like
> saying 3*7 = 25 on planet TETRA. They mean 3*7 = 21, they just put it
> differently.
Of course, symbolisms are arbitrary, but physical instantiation makes
all the difference.
> No problem. I see you assume a physical universe. I don't. We havejust
> different theories.
So, which experiment decides which is true? I think "platonism" derives
it's power from misconceptions of the human mind.
The unthinking stone would never construe such a thing as platonism.
It would just exist - in a very real world ;-)
>Note that if you understand the whole UDA,
Unfortunately, not yet, but I'm reading!
> you should realize that the
>price of assuming a physical universe (and wanting it to be related
>with our experiences *and* our experiments) is to postulate that you
>(and us, if you are not solipsistic) are not turing emulable. No
>problem.
Why is that so? Could you clarify this issue?
>(I like to separate issues concerning the choice of theory, and issues
>concerning propositions made *in* a theory, or accepting that theory).
Absolutely. But I think we have to start with our assumptions and
try to scrutinize them very carefully. After all, we want to devote
our minds to problems arising out of them during our lives, and
thus the initial choice should not be made rashly, but only after
careful review of our current body of knowledge.
Best Regards,
Günther
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Received on Wed Aug 16 2006 - 18:16:29 PDT